WLS-ENO Remap: Superconvergent and Non-Oscillatory Weighted Least Squares Data Transfer on Surfaces

TL;DR

This paper introduces WLS-ENOR, a high-order, non-oscillatory data remap method for surfaces that effectively handles discontinuities and achieves superconvergence in smooth regions.

Contribution

WLS-ENOR extends WLS-ENO by resolving both C0 and C1 discontinuity oscillations, introducing a robust detector and optimized weights for superconvergence and high accuracy.

Findings

WLS-ENOR achieves over fifth-order accuracy in smooth regions.

It effectively suppresses oscillations near discontinuities.

The method is highly conservative and minimally diffusive.

Abstract

Data remap between non-matching meshes is a critical step in multiphysics coupling using a partitioned approach. The data fields being transferred often have jumps in function values or derivatives. It is important but very challenging to avoid spurious oscillations (a.k.a. the Gibbs Phenomenon) near discontinuities and at the same time to achieve high-order accuracy away from discontinuities. In this work, we introduce a new approach, called WLS-ENOR, or Weighted-Least-Squares-based Essentially Non-Oscillatory Remap, to address this challenge. Based on the WLS-ENO reconstruction technique proposed by Liu and Jiao (J. Comput. Phys. vol 314, pp 749--773, 2016), WLS-ENOR differs from WLS-ENO and other WENO schemes in that it resolves not only the O(1) oscillations due to C 0 discontinuities, but also the accumulated effect of O(h) oscillations due to C 1 discontinuities. To this end, WLS-ENOR introduces a robust detector of discontinuities and a new weighting scheme for WLS-ENO near discontinuities. We also optimize the weights at smooth regions to achieve superconvergence. As a result, WLS-ENOR is more than fifth-order accurate and highly conservative in smooth regions, while being non-oscillatory and minimally diffusive near discontinuities. We also compare WLS-ENOR with some commonly used methods based on L 2 projection, moving least squares, and radial basis functions.